This algebra 2 probability rules test checks probability: sample spaces, independence and conditional probability in 45 minutes, with 9 questions for a total of 20 points.
This test covers sample spaces, events, the addition rule, independence, conditional probability, two-way tables and tree diagrams in Algebra 2. It has 9 questions worth 20 points. Allow 45 minutes, write fractions in lowest terms, and show your work for every answer.
- Grade: Algebra 2
- Chapter: Probability: Sample Spaces, Independence and Conditional Probability
- Common Core: S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 3 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 2 pts; Question 9: 1 pt)
Algebra 2 Probability Rules Test: questions 1–5
Question 1: Sample space of coin flips (2 points)
A fair coin is flipped three times .
- List all outcomes in the sample space. (1 point)
- Let \(A\) be “exactly two heads”. List the outcomes in \(A\) and find \(P(A)\). (1 point)
Question 2: Events from a set of numbers (2 points)
A number is chosen at random from \(1,2,3,…,12\) written on slips. Let \(A\) be “even number” and \(B\) be “multiple of \(3\)”.
- List the outcomes in “\(A\) and \(B\)” and in “\(A\) or \(B\)”. (1 point)
- Find \(P(A\text{ or }B)\) and \(P(\text{not }A)\). (1 point)
Question 3: Addition rule with a Venn diagram (2 points)
The Venn diagram shows \(40\) students in choir and drama. One student is chosen at random.
- Find \(P(\text{choir})\), \(P(\text{drama})\) and \(P(\text{choir and drama})\). (1 point)
- Use the addition rule to find \(P(\text{choir or drama})\), then find \(P(\text{neither})\). (1 point)
Question 4: Independent or not (2 points)
Events \(A\) and \(B\) have \(P(A)=0.3\) and \(P(B)=0.6\).
- If \(P(A\text{ and }B)=0.18\), are \(A\) and \(B\) independent? Justify your answer. (1 point)
- If instead \(P(A\text{ and }B)=0.2\), find \(P(A|B)\). (1 point)
Question 5: Two-way table of lunches (3 points)
The table shows \(120\) students by grade and lunch type. One student is chosen at random.
- Find \(P(\text{school lunch})\). (1 point)
- Find \(P(\text{10th}\,|\,\text{packed lunch})\). (1 point)
- Are “9th grade” and “school lunch” independent? Justify your answer. (1 point)
Algebra 2 Probability Rules Test: questions 6–9
Question 6: Pens without replacement (3 points)
A box holds \(4\) black pens and \(2\) white pens. Two pens are drawn without replacement. The tree shows the probabilities.
- Find the probability that both pens are black. (1 point)
- Find the probability that the pens have different colors. (1 point)
- Find the probability that the first pen is black, given that the second pen is white. (1 point)
Question 7: Free throws in a row (3 points)
Jamal makes \(80\%\) of his free throws, and his shots are independent. He takes two shots.
- Find the probability that he makes both. (1 point)
- Find the probability that he misses both. (1 point)
- Find the probability that he makes at least one. (1 point)
Question 8: Conditional probability formula (2 points)
In a town, \(60\%\) of households have a dog (\(D\)), \(40\%\) have a cat (\(C\)), and \(25\%\) have both.
- Find \(P(C|D)\). (1 point)
- Find \(P(D|C)\). (1 point)
Question 9: At least one six (1 point)
A fair die is rolled twice. Find the probability of getting at least one \(6\).
How to use this algebra 2 probability rules test
Take this algebra 2 probability rules test without notes, then grade it with the test answer key out of 20 points.
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Algebra 2 Probability: Sample Spaces, Independence and Conditional Probability test
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